Optical lens design for flattening a through-focus curve

ABSTRACT

Described herein are systems and/or methods for forming an ophthalmic lens. An example method may comprise a step of determining a power profile based on a power profile function defined by a base optical power, an amount of spherical aberration at a radial distance from a geometric center of the lens, and a bump function. The example method may comprise a step of adjusting the power profile based at least on minimizing a shape metric of a through-focus curve.

BACKGROUND

Myopia, presbyopia, and emerging presbyopia have high prevalence ratesin many regions of the world. One concern with myopia is its possibleprogression to high myopia, for example greater than five or sixdiopters, which dramatically affects one's ability to function withoutoptical aids. High myopia is also associated with an increased risk ofretinal disease, cataracts, and glaucoma. Moreover, lens wearers mayexperience asthenopia using conventional lenses.

WO/2012/173891 describers a central zone in a lens that is surrounded bya rapidly increasing power distribution generating a perceivable blur tothe user that causes an attendant increase in effective depth of focus.The depth of focus is increased to relieve stress from overallaccommodative effort and stress from accommodation and accommodative lagto retard myopia progression and enable continuous and long termtreatment by the user. However, improvements in lens design are needed.Additionally, or alternatively, improvements in correcting presbyopiaand/or emerging presbyopia are desired.

SUMMARY

Described herein are systems and/or methods for forming an ophthalmiclens. An example method may comprise a step of determining a powerprofile based on a power profile function defined by a base opticalpower, an amount of spherical aberration at a radial distance from ageometric center of the lens, and a bump function. A method may compriseforming a lens by configuring a main body of the lens such that at leastan intensity of light propagating through the lens is changed to exhibita target apodization profile. The intensity of light propagating throughthe lens may be changed by apodizing the lens. The example methods maycomprise a step of adjusting the power profile based at least onminimizing a shape metric (e.g., through-focus flatness metric,curvature, slope, RMS) of a through-focus curve. As an example, thepower profile may be configured based on flattening a through-focuscurve at or adjacent a target vergence. The example method may comprisea step of forming a lens to exhibit the adjusted power profile.

Described herein are systems and/or methods for forming an ophthalmiclens. An example ophthalmic lens may comprise a main body configured toexhibit a power profile based on a power profile function defined by abase optical power, an amount of spherical aberration at a radialdistance from a geometric center of the lens, and a bump function. Thepower profile may be optimized based at least on minimizing a shapemetric of a through-focus curve. In certain aspects, the bump functionmay comprise a multifocal function.

Described herein are systems and/or methods for forming an ophthalmiclens. An example ophthalmic lens may comprise a main body configured toexhibit a power profile based on a power profile function defined by abase optical power, an amount of spherical aberration at a radialdistance from a geometric center of the lens, and a bump function. Thepower profile may provide vision correction and may be further optimizedto slow myopia progression or treat emerging presbyopia or presbyopiabased at least on minimizing a shape metric of a through-focus curve.

Described herein are systems and/or methods for forming an ophthalmiclens. An example method may comprise a step of determining a powerprofile based on a power profile function defined by a base opticalpower, an amount of spherical aberration at a radial distance from ageometric center of the lens, and a bump function. The example methodmay comprise a step of adjusting the power profile based at least onminimizing a shape metric of a through-focus curve. The example methodmay comprise a step of forming a lens to exhibit the adjusted powerprofile.

The lenses, systems, and methods described herein may provide visioncorrection, which may be based on a wearer's need. The lenses, systems,and methods described herein may be effective in slowing myopiaprogression. The lenses, systems, and methods described herein may beeffective in treating presbyopia or emerging presbyopia.

BRIEF DESCRIPTION OF THE DRAWINGS

The following drawings show generally, by way of example, but not by wayof limitation, various examples discussed in the present disclosure. Inthe drawings:

FIG. 1 shows example correlations between a flatness of a through-focusretinal image quality and an observed axial length treatment efficacyfor different contact lens designs.

FIG. 2A shows example bump functions with adjusted center location.

FIG. 2B shows example bump functions with adjusted amplitude.

FIG. 2C shows example bump functions with adjusted width.

FIG. 2D shows example bump functions with adjusted flatness.

FIGS. 3A-3B show example plots of a power profile of a first exampledesign. In both plots, designs for subjects with six differentrefractive errors are shown, Rx=−9D, Rx=−6D, Rx=−3D, Rx=2D, Rx=4D,Rx=6D. FIG. 3A shows the power profile. FIG. 3B shows the power profilewith refraction subtracted to highlight the manner in which the designsmight vary with refraction.

FIG. 4 shows through-focus image quality curves about a near vergence of3D for the first example design and an example bifocal design (baselinelens).

FIG. 5 shows a model prediction on treatment efficacy of the firstexample design.

FIG. 6 shows an example plot of a transmittance profile of a secondexample design.

FIG. 7 shows through-focus image quality curves about a near vergence of3D for the second example design and an example bifocal design (baselinelens).

FIG. 8 shows a model prediction on treatment efficacy of the secondexample design.

FIG. 9 shows an example plot of a power profile of a third exampledesign.

FIG. 10 shows through-focus image quality curves about a near vergenceof 3D for the third example design and an example bifocal design(baseline lens).

FIG. 11 shows a model prediction on treatment efficacy of the thirdexample design.

FIG. 12 shows an example plot of a power profile of a fourth exampledesign.

FIG. 13 shows an example plot of a power profile of the baseline lens.

DETAILED DESCRIPTION

The present disclosure recognizes a relationship between flatness of athrough-focus curvature associated with a lens and the effectiveness forslowing myopia progression.

As an illustrative example, myopia can be thought of as occurringbecause the eye has grown too long for the focal length of the opticalsystem. It has been shown that near work is a significant risk factorfor the development and progression of myopia. Meanwhile, humans oftenexhibit accommodative lag or negative spherical aberration during nearwork, resulting in hyperopic blur. As a result, the eye grows to attemptto bring the image into focus, resulting in progression of myopia. Forthis to occur, the eye must have some mechanism for detecting the signof wavefront divergence, myopic or hyperopic. The asymmetry of the pointspread function through-focus may aid in the eye's ability to detect thesign of wavefront divergence, obtained through-focus by some othermechanism. The strength of that signal is then linked to the steepnessor flatness of the through-focus curve. A steeper through-focus curveresults in a stronger more reliable signal and a flatter curve resultsin a weaker signal. Thus, given that hyperopic blur is likely to bepresent, it may be desirable to attenuate the detected signal byproviding a flatter through-focus curve.

As such, novel lens designs and methods may take into account thisrelationship such that the formed lens may be used to provide visioncorrection and to slow myopia progression in a wearer. As described inthe present disclosure, lens designs may be configured to flattenthrough-focus curves, while providing functional vision correction. Itis noted that although bifocal lenses have also shown efficacy inslowing myopia progression, such bifocal lenses often sacrifice visualacuity. As described herein, lenses that have been configured withflatter through-focus curves (e.g., minimized shape metric of thethrough-focus curve), for example, by incorporating a particular bumpfunction as part of the power profile of a lens, provide improved visionover a bifocal lens (e.g., baseline lens having a power profile shown inFIG. 13), while demonstrating potential at slowing myopia progression.Example designs are also applicable in vision corrections for presbyopesor emerging presbyopes.

Described herein are systems and/or methods for forming an ophthalmiclens. An example method may comprise a step of determining a powerprofile based on a power profile function. The power profile functionmay be defined by a base optical power, an amount of sphericalaberration at a radial distance from a geometric center of the lens, anda bump function. The term bump function may be defined as a mathematicalrepresentation that results in a “bump” or deviation (e.g., increase) inand underlying curve. As an example, a bump function as used herein mayrepresent a bump or positive deviation in optical power in a discreteportion of a lens, for example, relative to radial position. Althoughthe term bump function is used, a multi-focal function creating aplurality of “bumps” in a resultant power profile may be used. As anillustrative example, spherical aberration and/or parameters of a bumpfunction may be configured based on a characteristic of a targetpopulation. A target population may comprise one or more individuals. Atarget population may comprise a plurality of eyes that have a commoncharacteristic. Example characteristics defining a target population maycomprise those having myopia progression (e.g., pediatrics with myopiaprogression) or those having emerging presbyopia. Such characteristicmay comprise pupil size or vergence variance, or prescription strength,or a combination. Other characteristics may be used. Characteristics maycomprise one or more of pupil size or vergence variance for a particularprescription.

The example method may comprise a step of adjusting the power profilebased at least on minimizing a shape metric (e.g., through-focusflatness metric, curvature, slope, RMS) of a through-focus curve. Theterm minimizing may be defined as a desire for the least amount ofdeviation at or near a target vergence. The term minimizing may bedefined as a desire for the least amount of deviation as represented bya desire to minimize a rate of change and extent of change of athrough-focus curve. However, a completely flat through-focus curve maynot provide appropriate vision correction and thus, a balance betweenfactors may be necessary. Thus, minimizing is not necessarily defined asthe minimum, but instead is used as a determinative factor toward aflatter curve, as described herein. As an example, one or more powerprofiles may be adjusted based on an increased flatness of the curvatureof an associated through-focus curve compared to the non-adjustedprofile.

As used herein, a through-focus flatness (TFF) metric may be defined by:

$\begin{matrix}{{{TFF} = {\int_{v_{t - \delta}}^{v_{t + \delta}}{{\frac{{df}(v)}{dv}}{dv}}}},} & (1)\end{matrix}$

where v_(t) is the target vergence, and δ is a vergence deviation aboutthe target vergence (in an example embodiment, δ is between 0.05 and0.3D including endpoints and intervening endpoints), f(v) is thethrough-focus visual performance (visual acuity) which, by definition,varies with vergence, v. Other ranges may be used. For example, δ may bebetween 0.1 and 0.3D (including endpoints and intervening endpoints, orδ may be between 0.001 and 0.10D including endpoints and interveningendpoints. For these purposes, v and δ are typically expressed in unitsof Diopters and f(v) is typically expressed in units of −10 log MAR. Thethrough-focus flatness metric used herein is the integral of theabsolute value of the derivative (the slope) of the through-focus visualperformance function taken around the target vergence. Thus, a smallerflatness metric corresponds to flatter through-focus visual performancenear the target vergence. Minimizing a shape metric of a through-focuscurve may comprise minimizing the through-focus flatness metric definedherein.

An example method may comprise a step of forming a lens to exhibit theadjusted power profile. Forming a lens may comprise configuring thegeometric shape of the lens. Forming a lens may comprise configuring theinternal gradient refractive index profile of the lens. Forming a lensmay comprise configuring the geometric shape of the lens and theinternal gradient refractive index profile of the lens. Forming a lensmay comprise configuring a main body of the lens such that lightpropagating through the lens is refracted to exhibit an adjusted powerprofile. The intensity of light propagating through the lens may bechanged through apodization. The apodization of the lens may be based ona transmittance profile, which may take any form. As an example, atransmittance profile may vary radially from the center of the lens. Asanother example, the transmittance profile may be based on theStiles-Crawford effect. As another example, the transmittance profilemay be or comprise a non-monotonically varying curve. The transmittancemay be higher at pupil center and may decrease radially outwardly fromthe center until an increase at or adjacent the optical zone edge. Thetransmittance profile may have a maximum transmittance at the center ofthe optical zone and a minimum transmittance positioned at a radius lessthan the optical zone radius. Other profiles may be used.

Described herein are systems and/or methods for forming an ophthalmiclens. An example ophthalmic lens may comprise a main body configured toexhibit a power profile based on a power profile function defined by abase optical power, an amount of spherical aberration at a radialdistance from a geometric center of the lens, and a bump function. Thepower profile may be optimized based at least on minimizing a shapemetric of a through-focus curve. The bump function may comprise amultifocal function. The main body may be configured by configuring thegeometric shape of the lens. The main body may be configured byconfiguring the internal gradient refractive index profile of the lens.The main body may be configured by configuring the geometric shape ofthe lens and the internal gradient refractive index profile of the lens.The main body may be configured such that light propagating through thelens is refracted to exhibit an adjusted power profile. The main bodymay be configured such that at least an intensity of light propagatingthrough the lens is changed to exhibit a target apodization profile. Theintensity of light propagating through the lens may be changed throughapodization. The apodization of the lens may be based on a transmittanceprofile which may take any form. As an example, the transmittanceprofile may vary radially from the center of the lens. As anotherexample, the transmittance profile may be based on the Stiles-Crawfordeffect. As another example, the transmittance profile may be or comprisea non-monotonically varying curve. The transmittance may be higher atpupil center and may decrease radially outwardly from the center untilan increase at or adjacent the optical zone edge. The transmittanceprofile may have a maximum transmittance at the center of the opticalzone and a minimum transmittance positioned at a radius less than theoptical zone radius. Other profiles may be used.

Described herein are systems and/or methods for forming an ophthalmiclens. An example ophthalmic lens may comprise a main body configured toexhibit a power profile based on a power profile function defined by abase optical power, an amount of spherical aberration at a radialdistance from a geometric center of the lens, and a bump function.

The power profile may provide vision correction and may be furtheroptimized to slow myopia progression or treat presbyopia or emergingpresbyopia based at least on minimizing a shape metric of athrough-focus curve. The main body may be configured by configuring thegeometric shape of the lens. The main body may be configured byconfiguring the internal gradient refractive index profile of the lens.The main body may be configured by configuring the geometric shape ofthe lens and the internal gradient refractive index profile of the lens.The main body may be configured such that light propagating through thelens is refracted to exhibit the power profile.

The main body may be configured such that at least an intensity of lightpropagating through the lens is changed to exhibit a target apodizationprofile. The intensity of light propagating through the lens may bechanged through apodization. The apodization of the lens may be based ona transmittance profile defined by a continuous function. Theapodization of the lens may be based on a transmittance profile whichmay take any form. As an example, the transmittance profile may varyradially from the center of the lens. As another example, thetransmittance profile may be based on the Stiles-Crawford effect. Asanother example, the transmittance profile may be or comprise anon-monotonically varying curve. The transmittance may be higher atpupil center and may decrease radially outwardly from the center untilan increase at or adjacent the optical zone edge. The transmittanceprofile may have a maximum transmittance at the center of the opticalzone and a minimum transmittance positioned at a radius less than theoptical zone radius. Other profiles may be used.

Described herein are systems and/or methods for forming an ophthalmiclens. An example method may comprise a step of determining a powerprofile based on a power profile function defined by a base opticalpower, an amount of spherical aberration at a radial distance from ageometric center of the lens, and a bump function. The example methodmay comprise a step of adjusting the power profile based at least onminimizing a shape metric of a through-focus curve. The example methodmay comprise a step of forming a lens to exhibit the adjusted powerprofile. Forming a lens may comprise configuring the geometric shape ofthe lens. Forming a lens may comprise configuring the internal gradientrefractive index profile of the lens. Forming a lens may compriseconfiguring the geometric shape of the lens and the internal gradientrefractive index profile of the lens. Forming a lens may compriseconfiguring a main body of the lens such that light propagating throughthe lens is refracted to exhibit an adjusted power profile.

Forming a lens may comprise configuring a main body of the lens suchthat at least an intensity of light propagating through the lens ischanged to exhibit a target apodization profile. The intensity of lightpropagating through the lens may be changed through apodization. Theapodization of the lens may be based on a transmittance profile whichmay take any form. As an example, the transmittance profile may varyradially from the center of the lens. As another example, thetransmittance profile may be based on the Stiles-Crawford effect. Asanother example, the transmittance profile may be or comprise anon-monotonically varying curve. The transmittance may be higher atpupil center and may decrease radially outwardly from the center untilan increase at or adjacent the optical zone edge. The transmittanceprofile may have a maximum transmittance at the center of the opticalzone and a minimum transmittance positioned at a radius less than theoptical zone radius. Other profiles may be used.

Other methods and lens design may be used.

EXAMPLES

Myopia typically occurs due to excessive axial growth or elongation ofthe eye. Based on animal research, axial eye growth may be influenced bythe quality and focus of the retinal image. One of the risk factors formyopia development in humans is near work. When young eyes look at anear object through a contact lens, the accommodation systems activelyadjust the crystal lens to form a sharp focal point on the retina orslightly behind the retina. The latest retinal image quality model,which takes into account three factors (accommodation system change,lens decentration, population aberration variation), found a correlationbetween the flatness of the through-focus retinal image quality andtreatment efficacy for different contact lens designs, as illustrated inFIG. 1.

FIG. 1 shows example correlations between a flatness of a through-focusretinal image quality and an observed treatment efficacy for differentcontact lens designs.

The power profile of current design may be described as follows:

p(r)=p ₀ +sa×r ²+Ψ(r),  (2)

wherein r represents a radial distance (millimeter (mm)) from ageometric lens center; p₀ represents the base power (diopters (D)) ofthe lens (e.g., the paraxial power which may comprise a spherical power,a cylindrical power, or a combination thereof); sa represents an amountof spherical aberration (D/mm²); p(r) represents the lens power profile;and Ψ(r) represents a bump function that is further described inequation (3).

$\begin{matrix}{{\Psi(r)} = \left\{ {\begin{matrix}{{\left( \frac{h}{\exp\left( {- 1} \right)} \right) \times {\exp\left( {- \frac{1}{1 - \left\lbrack \frac{\left( {r - r_{0}} \right)}{\left( {d/2} \right)} \right\rbrack^{2n}}} \right)}},} & {{{\left. {{r > {0\mspace{14mu}{and}\mspace{14mu} r}} \in} \right\rbrack r_{0}} - \frac{d}{2}},{r_{0} + {\frac{d}{2}\lbrack}}} \\{0,} & {otherwise}\end{matrix},} \right.} & (3)\end{matrix}$

wherein r represents a radial distance (mm) from a geometric lenscenter; h is the height (D) of the bump function; r₀ represents thecenter location (mm) of the bump function; d represents the width (mm)of the bump; and n is an integer such that n≥1 which represents theflatness of the bump.

FIGS. 2A-2D show example bump functions, and the role of each of thedefining parameters. Various example bump functions are plotted in FIGS.2A-2D. Comparing to a typical multifocal step, the power profile changeof the bump function is gradual and continuous. With this feature beingpart of the optical design, it is easier for the design to achievetarget vision correction with a relatively flat through-focus imagequality curve.

Table 1 shows parameter values for the power profile of an exampledesign for prescription Rx=−3D FIGS. 3A-3B show plots for the powerprofile of examples designs for subjects with six different refractiveerrors: Rx=−9D, Rx=−6D, Rx=−3D, Rx=2D, Rx=4D, Rx=6D. Rx denotes themanifest spherical refraction of the subject. FIG. 3A shows the powerprofile and FIG. 3B shows the power profiles with refraction subtractedto highlight the manner in which the designs might vary with refraction.

TABLE 1 Parameter Values of Design Example I (Design I). Parameters p₀sa h r₀ d Values −2.8 D −0.084 2.09 D 0.60 mm 1.80 mm D/mm{circumflexover ( )}2

In comparison with an example baseline lens with a power profile shownin FIG. 13, the simulated distance visual acuity of the new design(Design I) is approximately 1.2 lines of visual acuity better (VA−10 LogMAR). Moreover, as the through-focus curve of the new design is flatterthan that of the baseline lens (as illustrated in FIG. 4), this newdesign is expected to be more efficacious in slowing down myopiaprogression than the baseline lens (as modeled in FIG. 5).

In practice, depending on the aberration pattern of the young eye atdifferent accommodating states, the parameter ranges of the new designare summarized in Table 2 as follows:

TABLE 2 Parameter Ranges of Design Example I. Parameters p₀ sa h r₀ d nValues [−0.5, +0.5] [−0.05, 0.1] [0.1, 10] D [0.4, 1.4] mm [1.5, 2.1] mm[1, ∞] from the Rx D/mm{circumflex over ( )}2 Power

Equations 1 and 2 outline the power profile of a lens design. Inpractice, the design may be fabricated either by adjusting the geometricshape of the lens and/or by changing the internal gradient refractiveindex profile of the lens. As a result, the light propagating throughthe lens is refracted resulting in a desired power profile.

In addition, the light intensity may also be adjusted by the method ofapodizing the lens from the center to the periphery in transmittance.Such a transmittance profile may take any form and may vary radiallyfrom the center of the lens. For example, the transmittance profile maydecrease from the center of the lens to a middle point and then mayincrease again from the middle point to a peripheral point. As anotherexample, the transmittance profile may be based on the Stiles-Crawfordeffect. As another example, the transmittance profile may be or comprisea non-monotonically varying curve. The transmittance may be higher atpupil center and may decrease radially outwardly from the center untilan increase at or adjacent the optical zone edge. The transmittanceprofile may have a maximum transmittance at the center of the opticalzone and a minimum transmittance positioned at a radius less than theoptical zone radius. Other profiles may be used. The transmittanceprofile may be represented by many mathematical formulae or equationssuch as a piecewise cubic Hermite interpolating polynomial curvecontrolled by a series number of points (See Fritsch et al., MonotonePiecewise Cubic Interpolation, SIAM J. Numerical Analysis, Vol. 17,1980, pp. 238-46.) A transmittance profile may be defined by acontinuous function, with a non-monotonically varying transmittance. Asan example, a maximum of transmittance is at pupil center and a minimizevalue is positioned less than optical zone (OZ radius). As anotherexample, the transmittance is based on a polynomial function such as:

T=(−0.4179r{circumflex over ( )}7+5.1596r{circumflex over( )}6−24.399r{circumflex over ( )}5+54.5187r{circumflex over( )}4−57.4684r{circumflex over ( )}3+35.308r{circumflex over( )}2−46.6963r{circumflex over ( )}+100.1505)/100

A lens with such an apodization profile may be fabricated byincorporating light absorbing compounds into the reactive monomermixture from which the lens is made, by pad printing light absorbingpatterns onto the molds between which the lens is made which aresubsequently incorporated into the lens upon curing, by embedding rigidapodized inserts into the lens, by post-fabrication methods ofimpregnation or chemical grafting of light absorbing compounds into oronto the lens, or the like. The light absorbing compounds may bereactive or nonreactive, organic or organometallic dyes, coated oruncoated nanoparticles, or the like, and combinations thereof.

This disclosure provides an example design (Design II) that manipulatesthe light by refraction and apodization. The power profile of Design IIis the same as Design I. The parameter values used to describe the powerprofile of Design II are the same as those in Table 1. The controlpoints that describe the transmittance profile are summarized in Table3.

TABLE 3 Parameter Values (Intensity) of Design Example II (Design II).Parameters for Transmittance Point #1 Point #2 Point #3 Radial Position0 mm 1.75 mm 3.5 mm Transmittance 100% 57% 68%

The transmittance profile of Design II is shown in FIG. 6. As a resultof the combined features of power profile and transmittance apodizationprofile, the effectiveness of vision correction of the Design II issimilar, and slightly better, than Design I and better than the baselinelens. As an example, Design 2 modelled as −0.75 VA−10 Log MAR comparedto the baseline lens, which modelled as about −2 VA−10 Log MAR. However,as the through-focus curve of Design II is flatter than Design I (FIG. 7vs FIG. 4), Design II is expected to be more efficacious in slowing downmyopia progression than Design I and the baseline lens (FIG. 8 vs FIG.5).

Besides the bump design modality, multifocal design forms may also beused to yield the maximized balanced benefit of vision correction andtreatment efficacy in controlling myopia. These multifocal designs arealso applicable in vision corrections for presbyopes or emergingpresbyopes.

The power profile of multifocal designs may be described as follows:

p(r)=p ₀ +sa×r ² +M(r)  (4)

wherein r represents a radial distance from a geometric lens center; p₀represents the base power of the lens; sa represents an amount ofspherical aberration; p(r) represents the lens power profile; and M(r)represents a multifocal function that is further described in equation(5).

$\begin{matrix}{{M(r)} = \left\{ {\begin{matrix}{{addpower},} & {r_{1}^{\min} \leq r \leq r_{1}^{\max}} \\{{addpower},} & {r_{2}^{\min} \leq r \leq r_{2}^{\max}} \\{0,} & {otherwise}\end{matrix},} \right.} & (5)\end{matrix}$

wherein r represents a radial distance (mm) from a geometric lenscenter; r₁ ^(min) and r₁ ^(max) represent the locations of inner andouter boundaries of the 1^(st) add zone (mm); r₂ ^(min) and r₂ ^(max)represent the locations of inner and outer boundaries of the 2^(nd) addzone (mm); and addpower represents the magnitude of the add power (D).

Equations 4 and 5 may specify the power profile of a lens design. Inpractice, the design may be fabricated by adjusting the geometric shapeof the lens and/or by changing the internal gradient refractive indexprofile of the lens. As a result, light propagating through the lens isrefracted resulting in the desired power profile. Other methods may beused.

Alternatively, the power profile of multifocal designs may be describedas:

p(r)=p ₀ +sa×r ² +N(r),  (6)

wherein r represents a radial distance from a geometric lens center; p₀represents the base power of the lens; sa represents an amount ofspherical aberration; p(r) represents the lens power profile; and N(r)represents a bump multifocal function that is further described inequation (7).

$\begin{matrix}{{N(r)} = \left\{ {\begin{matrix}{{\Psi(r)},} & {r_{1}^{\min} \leq r \leq r_{1}^{\max}} \\{{\Psi(r)},} & {r_{2}^{\min} \leq r \leq r_{2}^{\max}} \\{0,} & {otherwise}\end{matrix},} \right.} & (7)\end{matrix}$

wherein r_(o1)=r₁ ^(min)+(r₁ ^(max)−r₁ ^(min))/2 represents the centerlocation of the first bump add zone; r_(o2)=r₂ ^(min)+(r₂ ^(max)−r₂^(min))/2 represents the center location of the first bump add zone.

The power profile of such an example multifocal design (Design III) (Rx:−3D) using equation (7) and the design parameters listed in Table 4 isshown in FIG. 9.

TABLE 4 Parameter Values of the example multifocal design. Parameters p₀sa r₁ ^(min) r₁ ^(max) r₂ ^(min) r₂ ^(max) addpower Values −3.0 D −0.061.2 mm 1.8 mm 2.25 mm 2.60 mm 1.5 D D/mm{circumflex over ( )}2

In comparison with the baseline lens, the simulated distance visualacuity of Design III is 1 letter better. Moreover, as the through-focuscurve of Design III is flatter than that of the baseline lens (FIG. 10),Design III is expected to be more efficacious in slowing down myopiaprogression than the baseline lens (FIG. 11).

In practice, depending on the aberration pattern of the young eye atdifferent accommodating states, the parameter ranges of the examplemultifocal design are summarized in the table as follows:

TABLE 5 Parameter Ranges of example multifocal design Parameters p₀ sar₁ ^(min) r₁ ^(max) r₂ ^(min) r₂ ^(max) addpower Values [−0.5, +0.5][−0.03, 0.09] [1.0, 1.4] [1.6, 2.0] [2.05, 2.45] [2.40, 2.80] [1.3, 1.7]D from the Rx D/mm{circumflex over ( )}2 mm mm mm mm Power

The above described designs are intended to flatten through-focus curvesand to maintain good vision correction. The designs are also applicablein vision corrections for presbyopes or emerging presbyopes. Therefore,the new Designs I, II, and III originally created for myopia control arealso applicable in correcting emerging presbyopia and presbyopia.

The power profile of another example design (Design IV) (Rx: −3D) usingequation (6) and design parameters listed in Table 6 for correctingemerging presbyopia (EP) is shown in FIG. 12.

TABLE 6 Parameter Values of EP Design Example. Parameters p₀ sa h r₀ dValues −2.91 D −0.02 0.2exp(1) 1.01 mm 1.47 mm D/mm{circumflex over( )}2 mm

Although shown and described in what is believed to be the mostpractical and preferred embodiments, it is apparent that departures fromspecific designs and methods described and shown will suggest themselvesto those skilled in the art and may be used without departing from thespirit and scope of the invention. The present invention is notrestricted to the particular constructions described and illustrated butshould be constructed to cohere with all modifications that may fallwithin the scope of the appended claims.

What is claimed is:
 1. An ophthalmic lens formed by a method comprising:determining a power profile based on a power profile function defined bya base optical power, an amount of spherical aberration at a radialdistance from a geometric center of a lens, and a bump function;adjusting the power profile based at least on minimizing a shape metricof a through-focus curve; and forming the lens to exhibit the adjustedpower profile.
 2. The lens of claim 1, wherein forming a lens comprisesconfiguring the geometric shape of the lens.
 3. The lens of claim 1,wherein the spherical aberration, and parameters of the bump functionare configured to vary by refractive prescription.
 4. The lens of claim1, wherein the spherical aberration, and parameters of the bump functionare configured based on a characteristic of a target population.
 5. Thelens of claim 4, wherein the characteristic is at least one of a pupilsize or a vergence variance.
 6. The lens of claim 1, wherein thespherical aberration, and parameters of the bump function are configuredbased on pupil size and vergence variances for a specific prescriptionor target population.
 7. The lens of claim 1, wherein forming a lenscomprises configuring the internal gradient refractive index profile ofthe lens.
 8. The lens of claim 1, wherein forming a lens comprisesconfiguring the geometric shape of the lens and the internal gradientrefractive index profile of the lens.
 9. The lens of claim 1, whereinforming a lens comprises configuring a main body of the lens such thatthe light propagating through the lens is refracted to exhibit theadjusted power profile.
 10. The lens of claim 1, wherein forming a lensfurther comprises configuring a main body of the lens such that at leastan intensity of light propagating through the lens is changed to exhibita target apodization profile.
 11. The lens of claim 10, wherein theintensity of light propagating through the lens is changed by apodizingthe lens.
 12. The lens of claim 11, wherein the apodizing the lens isbased on a transmittance profile defined by a continuous function, witha non-monotonically varying transmittance.
 13. The lens of claim 12,wherein a maximum of transmittance is at a pupil center and a minimumvalue is positioned less than optical zone (OZ) radius
 14. The lens ofclaim 13, wherein the transmittance is based on a polynomial function.15. The lens of claim 12, wherein a shape of the transmittance profilerelative to a radial position on the lens is defined by a decrease fromthe center to a midpoint and then an increase to a peripheral point. 16.The lens of claim 1, wherein the shape metric comprises a through-focusflatness (TFF) metric.
 17. The lens of claim 16, wherein the TFF isdefined by${TFF} = {\int_{v_{t - \delta}}^{v_{t + \delta}}{{\frac{{df}(v)}{dv}}{{dv}.}}}$18. An ophthalmic lens comprising: a main body configured to exhibit apower profile based on a power profile function defined by a baseoptical power, an amount of spherical aberration at a radial distancefrom a geometric center of a lens, and a bump function, wherein thepower profile is optimized based at least on minimizing a shape metricof a through-focus curve.
 19. The lens of claim 18, wherein the bumpfunction comprises a multifocal function.
 20. The lens of claim 18,wherein the spherical aberration, and parameters of the bump functionare configured to vary by refractive prescription.
 21. The lens of claim18, wherein the spherical aberration, and parameters of the bumpfunction are configured based on pupil size and vergence variances for aspecific prescription or target population.
 22. The lens of claim 18,wherein the main body is configured by configuring the geometric shapeof the lens.
 23. The lens of claim 18, wherein the main body isconfigured by configuring the internal gradient refractive index profileof the lens.
 24. The lens of claim 18, wherein the main body isconfigured by configuring the geometric shape of the lens and theinternal gradient refractive index profile of the lens.
 25. The lens ofclaim 18, wherein the main body is configured such that the lightpropagating through the lens is refracted to exhibit the power profile.26. The lens of claim 18, wherein the main body is configured such thatat least an intensity of light propagating through the lens is changedto exhibit a target apodization profile.
 27. The lens of claim 26,wherein the intensity of light propagating through the lens is changedby apodizing the lens.
 28. The lens of claim 27, wherein the apodizingthe lens is based on a transmittance profile defined by a continuousfunction, with a non-monotonically varying transmittance.
 29. The lensof claim 28, wherein a maximum of transmittance is at a pupil center anda minimum value is positioned less than optical zone (OZ) radius
 30. Thelens of claim 29, wherein the transmittance is based on a polynomialfunction.
 31. The lens of claim 28, wherein a shape of the transmittanceprofile relative to a radial position on the lens is defined by adecrease from the center to a midpoint and then an increase to aperipheral point.
 32. The lens of claim 18, wherein the shape metriccomprises a through-focus flatness (TFF) metric.
 33. The lens of claim32, wherein the TFF is defined by${TFF} = {\int_{v_{t - \delta}}^{v_{t + \delta}}{{\frac{{df}(v)}{dv}}{{dv}.}}}$34. An ophthalmic lens comprising: a main body configured to exhibit apower profile based on a power profile function defined by a baseoptical power, an amount of spherical aberration at a radial distancefrom a geometric center of a lens, and a bump function, wherein thepower profile provides vision correction and is further optimized toslow myopia progression or treat presbyopia based at least on minimizinga shape metric of a through-focus curve.
 35. The lens of claim 34,wherein the main body is configured by configuring the geometric shapeof the lens.
 36. The lens of claim 34, wherein the spherical aberration,and parameters of the bump function are configured to vary by refractiveprescription.
 37. The lens of claim 34, wherein the sphericalaberration, and parameters of the bump function are configured based onpupil size and vergence variances for a specific prescription or targetpopulation.
 38. The lens of claim 34, wherein the main body isconfigured by configuring the internal gradient refractive index profileof the lens.
 39. The lens of claim 34, wherein the main body isconfigured by configuring the geometric shape of the lens and theinternal gradient refractive index profile of the lens.
 40. The lens ofclaim 34, wherein the main body is configured such that the lightpropagating through the lens is refracted to exhibit the power profile.41. The lens of claim 34, wherein the main body is configured such thatat least an intensity of light propagating through the lens is changedto exhibit a target apodization profile.
 42. The lens of claim 41,wherein the intensity of light propagating through the lens is changedby apodizing the lens.
 43. The lens of claim 42, wherein the apodizingthe lens is based on a transmittance profile defined by a continuousfunction, with a non-monotonically varying transmittance.
 44. The lensof claim 43, wherein a maximum of transmittance is at a pupil center anda minimum value is positioned less than optical zone (OZ) radius
 45. Thelens of claim 44, wherein the transmittance is based on a polynomialfunction. The lens of claim 43, wherein a shape of the transmittanceprofile relative to a radial position on the lens is defined by adecrease from the center to a midpoint and then an increase to aperipheral point.
 46. The lens of claim 34, wherein the shape metriccomprises a through-focus flatness (TFF) metric.
 47. The lens of claim47, wherein the TFF is defined by${TFF} = {\int_{v_{t - \delta}}^{v_{t + \delta}}{{\frac{{df}(v)}{dv}}{{dv}.}}}$48. A method of forming an ophthalmic lens, the method comprising:determining a power profile based on a power profile function defined bya base optical power, an amount of spherical aberration at a radialdistance from a geometric center of a lens, and a bump function;adjusting the power profile based at least on minimizing a shape metricof a through-focus curve; and forming a lens to exhibit the adjustedpower profile.
 49. The method of claim 48, wherein forming a lenscomprises configuring the geometric shape of the lens.
 50. The method ofclaim 48, wherein the spherical aberration, and parameters of the bumpfunction are configured to vary by refractive prescription.
 51. Themethod of claim 48, wherein the spherical aberration, and parameters ofthe bump function are configured based on pupil size and vergencevariances for a specific prescription or target population.
 52. Themethod of claim 48, wherein forming a lens comprises configuring theinternal gradient refractive index profile of the lens.
 53. The methodof claim 48, wherein forming a lens comprises configuring the geometricshape of the lens and the internal gradient refractive index profile ofthe lens.
 54. The method of claim 48, wherein forming a lens comprisesconfiguring a main body of the lens such that the light propagatingthrough the lens is refracted to exhibit the adjusted power profile. 55.The method of claim 48, wherein forming a lens comprises configuring amain body of the lens such that at least an intensity of lightpropagating through the lens is changed to exhibit a target apodizationprofile.
 56. The method of claim 55, wherein the intensity of lightpropagating through the lens is changed by apodizing the lens.
 57. Themethod of claim 56, wherein the apodizing the lens is based on atransmittance profile defined by a continuous function, with anon-monotonically varying transmittance.
 58. The method of claim 57,wherein a maximum of transmittance is at a pupil center and a minimumvalue is positioned less than optical zone (OZ) radius
 59. The method ofclaim 58, wherein the transmittance is based on a polynomial function.60. The method of claim 57, wherein a shape of the transmittance profilerelative to a radial position on the lens is defined by a decrease fromthe center to a midpoint and then an increase to a peripheral point. 61.The method of claim 48, wherein the shape metric comprises athrough-focus flatness (TFF) metric.
 62. The method of claim 61, whereinthe TFF metric is defined by${TFF} = {\int_{v_{t - \delta}}^{v_{t + \delta}}{{\frac{{df}(v)}{dv}}{{dv}.}}}$